Problem: On the first 6 exams of her geometry class, Umaima got an average score of 83. What does she need on the next exam to have an overall average of 85?
Let her score on the next exam be $x$ The sum of all of her scores is then $6 \cdot 83 + x$ The same sum must also be equal to $7 \cdot 85$ Solve: $x = 7 \cdot 85 - 6 \cdot 83 = 97$.